# Neutral kaon semileptonic decays, why is $\overline{K^0}\rightarrow l^+\nu\pi^-$ not allowed?

On several texts it is stated that the semileptonic decays are different for the $K^0$ and $\overline{K^0}$, and each only gives leptons of particular charges (see www.hep.ph.ic.ac.uk/~dauncey/will/lecture16.pdf).

The allowed decays are $K^0\rightarrow l^+\nu\pi^-$ and $\overline{K^0}\rightarrow l^-\bar{\nu}\pi^+$ while $\overline{K^0}\not\rightarrow l^+\nu\pi^-$ and $K^0\not\rightarrow l^-\bar{\nu}\pi^+$.

Are $\overline{K^0}\rightarrow l^+\nu\pi^-$ and $K^0\rightarrow l^-\bar{\nu}\pi^+$ not allowed or only very suppressed with respect to the other semyleptonic decays? Why is the following diagram wrong/not allowed?

• The leptons carry the charge of the virtual W emitted by the s or $\bar s$ involved. Can you write down the quark content of your states that you learned in your particle physics course and monitor this charge flow? – Cosmas Zachos Oct 21 '17 at 21:49
• In fact, I see your reference does just that and rightly calls the rule obvious. Can you explain in your question what you do and do not understand about that? This is the unique way to conserve charge in every W vertex, no? – Cosmas Zachos Oct 21 '17 at 21:55
• Yes, quite clear. Your now proposed doubly weak decay is allowed, of course, but suppressed prodigiously w.r.t. the singly weak one your text considers. Can you estimate by how much? – Cosmas Zachos Oct 21 '17 at 23:50

To lowest order in the electroweak coupling these processes are given by a sequence of subprocesses like: $$q_1\to W^* q_2 \to (l \nu_l)q_2$$ $W^*$ is an off shell W boson. Take a look at the flavour content of the hadrons involved and the quarks that are being held responsible for the decays. What values can the charges of the W bosons have in each case?
• Thanks for your answer. I understand why the main decay of $K^0$ does not involve a negative lepton. I just wanted to know if the diagram I wrote is allowed (even if being very suppressed with respect to the other one). – Mil Oct 28 '17 at 14:08